Note 1.—The operation may frequently be considerably abridged, by dividing the 1st and 2nd, or the 1st and 3rd terms, by any number which will exactly divide them, afterwards using the quotients, instead of the numbers themselves.*
Example.—If 2 tons of iron for ordnance cost £40, how many tons may be bought for £360?
As £40 : £360 :: 2 tons : 18 tons.
(Thus 360 × 2) ÷ 40 = 18. The answer.
* Or thus, 9 × 2 = 18. The answer.
Note 2.—A concise method of ascertaining the annual amount of a daily sum of money.
Rule.—Bring the daily sum into pence, and then add together as many pounds, half pounds, groats, and pence, as there are pence in the daily sum, for the amount required. For leap year, add the rate for one day.
Example.—Required the annual amount of 2s. 6d. per diem.
| 2s. 6d. = 30d. | 30 pounds. | |
| 15 = | 30 half pounds. | |
| 10s. = 30 groats. | ||
| 2s. 6d. = 30 pence. | ||
| Annual amount (365 days) ... £45 12s. 6d. | ||
Note 3.—To find the amount of any number of days’ pay, the daily rate (under twenty shillings) being given.
The price of any article being given, the value of any number may be ascertained in a similar manner.
Rule 1. When the rate (or price) is an even number, multiply the given number by half of the rate, doubling the first figure to the right hand for the shillings, the remainder of the product will be pounds.